To proceed further—to compute the accessible information
and the associated redundancy—we need to specify a model
or class of models that provide the global states of interest. The
everyday photon environment has a particular structure where independent
environment components (photons) scatter off objects, acquire an imprint
of the state, and transmit that information onward, interacting little
with each other in the process [1]}, [2]}, [3]}, [4]}, [5]}, [6]}.
This structure is captured by purely decohering Hamiltonians by independent
environment components. I will consider this general class here. Under
this evolution, the quantum Chernoff bound (QCB) provides a universal
lower bound to the accessible information and the associated redundancy.
The quantum Chernoff result is also meaningful on its own as a single-shot
result quantifying how well an individual observer (with the best
measurement apparatus) can learn the pointer state of \(\mathcal {S}\)  indirectly
from \(\mathcal {F}\) .
